Express 90% confidence intervals and distribution shapes separately

[NunoSempere]

Proposal

Right now, distribution shapes are expressed as normal(mean, std), or beta(parameter 1, parameter 2). But it seems more natural to me to express the thought "a distribution shaped like a normal with 90% confidence interval as 20 to 30".

The syntax x to y could still default to doing this for the longnormal, but I'd still want a way to do this for other distributions.

Syntax ideas

I am not very sure about this, but we could express this as distributionShape(x to y) to mean "a distribution of that shape, with a confidence interval ranging from x to y". Other options might be to use different types of parenthesis or some other syntax, e.g., distributionShape(1..10), distributionShape(1~10), etc.

[OAGr]

My guess at this point is that few people will want shapes other than a few options (normal, lognormal, 1-3 more). It could still be good though. I'm not sure what the best syntax is, really curious.

If we allow people to write small libraries, then they could come up with their own custom syntaxes, for functions.

[OAGr]

How about,
normal({p5: 5, p95: 30})?
Similarly, we could do,
normal({mean: 5, stdev:5})
or normal({mean: 5, variance: 5})

We could do similar for other distributions that allow such functions.

[Hazelfire]

Just came across a need for this sort of thing. Something like lognormal({from: 3, to: 27, percentile: 0.5}) (50% confidence interval between two numbers) would be helpful in my work on existential risk estimates. Would like to chat here about how that could be implemented before going any further with it.

[alexlyzhov]

The most useful thing for me that currently doesn't seem implemented is to go from an arbitrary number of percentiles to a distribution. E.g. I specify 10th, 50th, and 90th percentile. Or I specify a rough shape of the distribution, specify the median, and then adjust the mass by recursively bisecting the space (e.g. then I go with 25th and 75th percentiles, then I do 12.5th and 37.5th, or something like that).

[OAGr]

Much of that sounds like stuff that the Metalog distribution should be able to help with. (@Hazelfire has been working on that)